Check if a large number is divisible by 5 or not

Given a number, the task is to check if number is divisible by 5. The input number may be large and it may not be possible to store even if we use long long int.

Examples: 

Input  : n = 56945255
Output : Yes

Input  : n = 1234567589333150
Output : Yes

Input  : n = 3635883959606670431112222
Output : No

Since input number may be very large, we cannot use n % 5 to check if a number is divisible by 5 or not, especially in languages like C/C++. The idea is based on following fact. 

   A number is divisible by 5 if its  
   digits last digit will be 0 or 5 .

Illustration: 

For example, let us consider 769555 
Number formed by last digit is = 5
Since 5 is divisible by 5 , answer is YES.

How does this work? 

Let us consider 5335, we can write it as
5335 = 5*1000 + 3*100 + 3*10 + 5

The proof is based on below observation:
Remainder of 10i divided by 5 is 0 if i greater 
than or equal to one. Note than 10, 100, 1000,
... etc lead to remainder 0 when divided by 5.

So remainder of " 5*1000 + 3*100 + 
3*10 + 5" divided by 5 is equivalent to remainder 
of following : 
0 + 0 + 0 + 5 = 5

Since 5 is divisible by 5, answer is yes.

Below is the implementation of above idea.

C++

// C++ program to find if a number is
// divisible by 5 or not
#include<bits/stdc++.h>
using namespace std;

// Function to find that number divisible
// by 5 or not. The function assumes that
// string length is at least one.
bool isDivisibleBy5(string str)
{
    int n = str.length();

    return ( ((str[n-1]-'0') == 0) ||
             ((str[n-1]-'0') == 5));
}

// Driver code
int main()
{
    string str = "76955";
    isDivisibleBy5(str)?  cout << "Yes" :
                          cout << "No ";
    return 0;
}

Java

// Java program to find if a number is
// divisible by 5 or not
import java.io.*;
class IsDivisible
{
    // Function to find that number divisible
    // by 5 or not. The function assumes that
    // string length is at least one.
    static boolean isDivisibleBy5(String str)
    {
        int n = str.length();

        return ( ((str.charAt(n-1)-'0') == 0) ||
                 ((str.charAt(n-1)-'0') == 5));
    }

    // main function
    public static void main (String[] args)
    {
        String str = "76955";
        if(isDivisibleBy5(str))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}

Python3

# Python program to find if a number is
# divisible by 5 or not

# Function to find that number divisible
# by 5 or not. The function assumes that
# string length is at least one.
def isDivisibleBy5(st) :
    n = len(st)
    return ( (st[n-1] == '0') or
           (st[n-1] == '5'))

# Driver code
st = "76955"
if isDivisibleBy5(st) :
    print ("Yes")
else :
    print ("No")

# This code is contributed by Nikita Tiwari.

C#

// C# program to find if a number is
// C# program to find if a number
// is divisible by 5 or not.
using System;

class IsDivisible
{
    // Function to find that number divisible
    // by 5 or not. The function assumes that
    // string length is at least one.
    static bool isDivisibleBy5(String str)
    {
        int n = str.Length;

        return (((str[n - 1] - '0') == 0) ||
                ((str[n - 1] - '0') == 5));
    }

    // Driver Code
    public static void Main ()
    {
        String str = "76955";
        if(isDivisibleBy5(str))
        Console.Write("Yes");
        else
        Console.Write("No");
    }
}

// This code is contributed by Nitin Mittal.

PHP

<?php
// PHP program to find if a number
// is divisible by 5 or not

// Function to find that number divisible
// by 5 or not. The function assumes that
// string length is at least one.
function isDivisibleBy5($str)
{
    $n = strlen($str);

    return ( (($str[$n-1]-'0') == 0) ||
            (($str[$n-1]-'0') == 5));
}

// Driver code
$str = "76955";
$x = isDivisibleBy5($str) ? "Yes" : "No";
echo($x);

// This code is contributed by Ajit.
?>

Javascript

<script>

// Javascript program to find if a number
// is divisible by 5 or not

// Function to find that number divisible
// by 5 or not. The function assumes that
// string length is at least one.
function  isDivisibleBy5(str)
{
    n = str.length;

    return (((str[n - 1] - '0') == 0) ||
            ((str[n - 1] - '0') == 5));
}

// Driver Code
var str = "76955";
var x = isDivisibleBy5(str) ? "Yes" : "No";

document.write(x);

// This code is contributed by bunnyram19

</script>

Output

Yes

Time Complexity: O(1), as we are not using any loops for traversing.
Auxiliary Space: O(1), as we are not using any extra space.
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